An algebraic approach to image de-smearing: Symmetries of polynomials and their zeros

Frequently a photograph received from a spacecraft will be smeared by some process, e.g., by camera motion. Algebraically such smearing can be represented as p = sigma f, where sigma is the true picture, p is the received picture, and f is the smearing function. (p, sigma, and f are polynomials in two variables x and y.) Thus, in principle, sigma can be recovered by multiplying p by 1/f. However, there are problems involved in computing 1/f. Some of these problems are investigated.